1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 475,801 x 11
##    site_type date       sex    age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr>  <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 female miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 female miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 female 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 female 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 female 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 female 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 female 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 female 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 female 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 female 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 475,791 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     63
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      6
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      8
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      8
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      9
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     11
## 250   2020-11-05          East of England     12
## 251   2020-11-06          East of England     19
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     16
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     24
## 266   2020-11-21          East of England     19
## 267   2020-11-22          East of England     21
## 268   2020-11-23          East of England     18
## 269   2020-11-24          East of England     21
## 270   2020-11-25          East of England     19
## 271   2020-11-26          East of England     19
## 272   2020-11-27          East of England     14
## 273   2020-11-28          East of England     28
## 274   2020-11-29          East of England     19
## 275   2020-11-30          East of England     22
## 276   2020-12-01          East of England     26
## 277   2020-12-02          East of England     18
## 278   2020-12-03          East of England     24
## 279   2020-12-04          East of England     25
## 280   2020-12-05          East of England     25
## 281   2020-12-06          East of England     22
## 282   2020-12-07          East of England     16
## 283   2020-12-08          East of England     26
## 284   2020-12-09          East of England     20
## 285   2020-12-10          East of England     32
## 286   2020-12-11          East of England     32
## 287   2020-12-12          East of England     27
## 288   2020-12-13          East of England     25
## 289   2020-12-14          East of England     32
## 290   2020-12-15          East of England     35
## 291   2020-12-16          East of England     29
## 292   2020-12-17          East of England     44
## 293   2020-12-18          East of England     44
## 294   2020-12-19          East of England     54
## 295   2020-12-20          East of England     52
## 296   2020-12-21          East of England     66
## 297   2020-12-22          East of England     52
## 298   2020-12-23          East of England     62
## 299   2020-12-24          East of England     61
## 300   2020-12-25          East of England     58
## 301   2020-12-26          East of England     64
## 302   2020-12-27          East of England     54
## 303   2020-12-28          East of England     71
## 304   2020-12-29          East of England     54
## 305   2020-12-30          East of England     76
## 306   2020-12-31          East of England     82
## 307   2021-01-01          East of England     90
## 308   2021-01-02          East of England     66
## 309   2021-01-03          East of England     78
## 310   2021-01-04          East of England     88
## 311   2021-01-05          East of England    102
## 312   2021-01-06          East of England    100
## 313   2021-01-07          East of England    116
## 314   2021-01-08          East of England     97
## 315   2021-01-09          East of England    133
## 316   2021-01-10          East of England    125
## 317   2021-01-11          East of England    126
## 318   2021-01-12          East of England    131
## 319   2021-01-13          East of England    131
## 320   2021-01-14          East of England    128
## 321   2021-01-15          East of England    119
## 322   2021-01-16          East of England    132
## 323   2021-01-17          East of England    133
## 324   2021-01-18          East of England    120
## 325   2021-01-19          East of England    130
## 326   2021-01-20          East of England    147
## 327   2021-01-21          East of England    136
## 328   2021-01-22          East of England    123
## 329   2021-01-23          East of England    102
## 330   2021-01-24          East of England    101
## 331   2021-01-25          East of England    114
## 332   2021-01-26          East of England     89
## 333   2021-01-27          East of England     94
## 334   2021-01-28          East of England    110
## 335   2021-01-29          East of England     96
## 336   2021-01-30          East of England     85
## 337   2021-01-31          East of England     74
## 338   2021-02-01          East of England     67
## 339   2021-02-02          East of England     75
## 340   2021-02-03          East of England     82
## 341   2021-02-04          East of England     75
## 342   2021-02-05          East of England     66
## 343   2021-02-06          East of England     78
## 344   2021-02-07          East of England     62
## 345   2021-02-08          East of England     73
## 346   2021-02-09          East of England     63
## 347   2021-02-10          East of England     53
## 348   2021-02-11          East of England     52
## 349   2021-02-12          East of England     47
## 350   2021-02-13          East of England     47
## 351   2021-02-14          East of England     33
## 352   2021-02-15          East of England     48
## 353   2021-02-16          East of England     47
## 354   2021-02-17          East of England     46
## 355   2021-02-18          East of England     31
## 356   2021-02-19          East of England     28
## 357   2021-02-20          East of England     31
## 358   2021-02-21          East of England     25
## 359   2021-02-22          East of England     26
## 360   2021-02-23          East of England     28
## 361   2021-02-24          East of England     18
## 362   2021-02-25          East of England     23
## 363   2021-02-26          East of England     15
## 364   2021-02-27          East of England     23
## 365   2021-02-28          East of England     17
## 366   2021-03-01          East of England     18
## 367   2021-03-02          East of England     19
## 368   2021-03-03          East of England     12
## 369   2021-03-04          East of England     19
## 370   2021-03-05          East of England     13
## 371   2021-03-06          East of England     12
## 372   2021-03-07          East of England     16
## 373   2021-03-08          East of England     15
## 374   2021-03-09          East of England     12
## 375   2021-03-10          East of England      9
## 376   2021-03-11          East of England     11
## 377   2021-03-12          East of England      4
## 378   2021-03-13          East of England     10
## 379   2021-03-14          East of England      6
## 380   2021-03-15          East of England      6
## 381   2021-03-16          East of England      8
## 382   2021-03-17          East of England      6
## 383   2021-03-18          East of England      2
## 384   2021-03-19          East of England      4
## 385   2021-03-20          East of England      4
## 386   2021-03-21          East of England      7
## 387   2021-03-22          East of England      2
## 388   2021-03-23          East of England      2
## 389   2020-03-01                   London      0
## 390   2020-03-02                   London      0
## 391   2020-03-03                   London      0
## 392   2020-03-04                   London      0
## 393   2020-03-05                   London      0
## 394   2020-03-06                   London      1
## 395   2020-03-07                   London      0
## 396   2020-03-08                   London      0
## 397   2020-03-09                   London      1
## 398   2020-03-10                   London      0
## 399   2020-03-11                   London      5
## 400   2020-03-12                   London      6
## 401   2020-03-13                   London     10
## 402   2020-03-14                   London     13
## 403   2020-03-15                   London      9
## 404   2020-03-16                   London     15
## 405   2020-03-17                   London     23
## 406   2020-03-18                   London     28
## 407   2020-03-19                   London     25
## 408   2020-03-20                   London     44
## 409   2020-03-21                   London     49
## 410   2020-03-22                   London     54
## 411   2020-03-23                   London     63
## 412   2020-03-24                   London     86
## 413   2020-03-25                   London    112
## 414   2020-03-26                   London    130
## 415   2020-03-27                   London    130
## 416   2020-03-28                   London    123
## 417   2020-03-29                   London    145
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## 1448  2020-12-09 North East and Yorkshire     50
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## 1451  2020-12-12 North East and Yorkshire     55
## 1452  2020-12-13 North East and Yorkshire     51
## 1453  2020-12-14 North East and Yorkshire     49
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## 1456  2020-12-17 North East and Yorkshire     49
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## 1460  2020-12-21 North East and Yorkshire     35
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## 1463  2020-12-24 North East and Yorkshire     50
## 1464  2020-12-25 North East and Yorkshire     57
## 1465  2020-12-26 North East and Yorkshire     67
## 1466  2020-12-27 North East and Yorkshire     73
## 1467  2020-12-28 North East and Yorkshire     64
## 1468  2020-12-29 North East and Yorkshire     58
## 1469  2020-12-30 North East and Yorkshire     42
## 1470  2020-12-31 North East and Yorkshire     51
## 1471  2021-01-01 North East and Yorkshire     71
## 1472  2021-01-02 North East and Yorkshire     60
## 1473  2021-01-03 North East and Yorkshire     49
## 1474  2021-01-04 North East and Yorkshire     64
## 1475  2021-01-05 North East and Yorkshire     64
## 1476  2021-01-06 North East and Yorkshire     61
## 1477  2021-01-07 North East and Yorkshire     73
## 1478  2021-01-08 North East and Yorkshire     68
## 1479  2021-01-09 North East and Yorkshire     58
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## 1483  2021-01-13 North East and Yorkshire     77
## 1484  2021-01-14 North East and Yorkshire     71
## 1485  2021-01-15 North East and Yorkshire     97
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## 1488  2021-01-18 North East and Yorkshire     83
## 1489  2021-01-19 North East and Yorkshire    104
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## 1491  2021-01-21 North East and Yorkshire     87
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## 1514  2021-02-13 North East and Yorkshire     53
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## 1518  2021-02-17 North East and Yorkshire     48
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## 1529  2021-02-28 North East and Yorkshire     29
## 1530  2021-03-01 North East and Yorkshire     19
## 1531  2021-03-02 North East and Yorkshire     17
## 1532  2021-03-03 North East and Yorkshire     28
## 1533  2021-03-04 North East and Yorkshire     17
## 1534  2021-03-05 North East and Yorkshire     28
## 1535  2021-03-06 North East and Yorkshire     21
## 1536  2021-03-07 North East and Yorkshire     19
## 1537  2021-03-08 North East and Yorkshire     20
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## 1542  2021-03-13 North East and Yorkshire     14
## 1543  2021-03-14 North East and Yorkshire     12
## 1544  2021-03-15 North East and Yorkshire     13
## 1545  2021-03-16 North East and Yorkshire     11
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## 1547  2021-03-18 North East and Yorkshire      8
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## 1549  2021-03-20 North East and Yorkshire     10
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## 1554  2020-03-02               North West      0
## 1555  2020-03-03               North West      0
## 1556  2020-03-04               North West      0
## 1557  2020-03-05               North West      1
## 1558  2020-03-06               North West      0
## 1559  2020-03-07               North West      0
## 1560  2020-03-08               North West      1
## 1561  2020-03-09               North West      0
## 1562  2020-03-10               North West      0
## 1563  2020-03-11               North West      0
## 1564  2020-03-12               North West      2
## 1565  2020-03-13               North West      3
## 1566  2020-03-14               North West      1
## 1567  2020-03-15               North West      4
## 1568  2020-03-16               North West      2
## 1569  2020-03-17               North West      4
## 1570  2020-03-18               North West      6
## 1571  2020-03-19               North West      7
## 1572  2020-03-20               North West     10
## 1573  2020-03-21               North West     11
## 1574  2020-03-22               North West     13
## 1575  2020-03-23               North West     15
## 1576  2020-03-24               North West     21
## 1577  2020-03-25               North West     21
## 1578  2020-03-26               North West     29
## 1579  2020-03-27               North West     36
## 1580  2020-03-28               North West     28
## 1581  2020-03-29               North West     46
## 1582  2020-03-30               North West     67
## 1583  2020-03-31               North West     52
## 1584  2020-04-01               North West     86
## 1585  2020-04-02               North West     96
## 1586  2020-04-03               North West     95
## 1587  2020-04-04               North West     98
## 1588  2020-04-05               North West    102
## 1589  2020-04-06               North West    100
## 1590  2020-04-07               North West    136
## 1591  2020-04-08               North West    127
## 1592  2020-04-09               North West    119
## 1593  2020-04-10               North West    117
## 1594  2020-04-11               North West    138
## 1595  2020-04-12               North West    125
## 1596  2020-04-13               North West    130
## 1597  2020-04-14               North West    130
## 1598  2020-04-15               North West    114
## 1599  2020-04-16               North West    135
## 1600  2020-04-17               North West     98
## 1601  2020-04-18               North West    114
## 1602  2020-04-19               North West     71
## 1603  2020-04-20               North West     83
## 1604  2020-04-21               North West     76
## 1605  2020-04-22               North West     87
## 1606  2020-04-23               North West     85
## 1607  2020-04-24               North West     67
## 1608  2020-04-25               North West     67
## 1609  2020-04-26               North West     55
## 1610  2020-04-27               North West     54
## 1611  2020-04-28               North West     57
## 1612  2020-04-29               North West     64
## 1613  2020-04-30               North West     60
## 1614  2020-05-01               North West     45
## 1615  2020-05-02               North West     56
## 1616  2020-05-03               North West     55
## 1617  2020-05-04               North West     48
## 1618  2020-05-05               North West     49
## 1619  2020-05-06               North West     44
## 1620  2020-05-07               North West     50
## 1621  2020-05-08               North West     43
## 1622  2020-05-09               North West     31
## 1623  2020-05-10               North West     42
## 1624  2020-05-11               North West     35
## 1625  2020-05-12               North West     38
## 1626  2020-05-13               North West     25
## 1627  2020-05-14               North West     26
## 1628  2020-05-15               North West     33
## 1629  2020-05-16               North West     32
## 1630  2020-05-17               North West     24
## 1631  2020-05-18               North West     31
## 1632  2020-05-19               North West     35
## 1633  2020-05-20               North West     27
## 1634  2020-05-21               North West     28
## 1635  2020-05-22               North West     26
## 1636  2020-05-23               North West     31
## 1637  2020-05-24               North West     26
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## 1639  2020-05-26               North West     27
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## 1641  2020-05-28               North West     28
## 1642  2020-05-29               North West     20
## 1643  2020-05-30               North West     19
## 1644  2020-05-31               North West     13
## 1645  2020-06-01               North West     12
## 1646  2020-06-02               North West     27
## 1647  2020-06-03               North West     22
## 1648  2020-06-04               North West     22
## 1649  2020-06-05               North West     16
## 1650  2020-06-06               North West     26
## 1651  2020-06-07               North West     20
## 1652  2020-06-08               North West     23
## 1653  2020-06-09               North West     17
## 1654  2020-06-10               North West     16
## 1655  2020-06-11               North West     16
## 1656  2020-06-12               North West     11
## 1657  2020-06-13               North West     10
## 1658  2020-06-14               North West     15
## 1659  2020-06-15               North West     16
## 1660  2020-06-16               North West     16
## 1661  2020-06-17               North West     13
## 1662  2020-06-18               North West     14
## 1663  2020-06-19               North West      7
## 1664  2020-06-20               North West     11
## 1665  2020-06-21               North West      8
## 1666  2020-06-22               North West     11
## 1667  2020-06-23               North West     13
## 1668  2020-06-24               North West     13
## 1669  2020-06-25               North West     15
## 1670  2020-06-26               North West      6
## 1671  2020-06-27               North West      7
## 1672  2020-06-28               North West      9
## 1673  2020-06-29               North West      9
## 1674  2020-06-30               North West      7
## 1675  2020-07-01               North West      3
## 1676  2020-07-02               North West      6
## 1677  2020-07-03               North West      7
## 1678  2020-07-04               North West      4
## 1679  2020-07-05               North West      6
## 1680  2020-07-06               North West      9
## 1681  2020-07-07               North West      8
## 1682  2020-07-08               North West      5
## 1683  2020-07-09               North West     10
## 1684  2020-07-10               North West      2
## 1685  2020-07-11               North West      5
## 1686  2020-07-12               North West      0
## 1687  2020-07-13               North West      6
## 1688  2020-07-14               North West      4
## 1689  2020-07-15               North West      5
## 1690  2020-07-16               North West      2
## 1691  2020-07-17               North West      4
## 1692  2020-07-18               North West      5
## 1693  2020-07-19               North West      3
## 1694  2020-07-20               North West      0
## 1695  2020-07-21               North West      2
## 1696  2020-07-22               North West      3
## 1697  2020-07-23               North West      3
## 1698  2020-07-24               North West      1
## 1699  2020-07-25               North West      1
## 1700  2020-07-26               North West      3
## 1701  2020-07-27               North West      1
## 1702  2020-07-28               North West      1
## 1703  2020-07-29               North West      2
## 1704  2020-07-30               North West      2
## 1705  2020-07-31               North West      0
## 1706  2020-08-01               North West      2
## 1707  2020-08-02               North West      1
## 1708  2020-08-03               North West      8
## 1709  2020-08-04               North West      3
## 1710  2020-08-05               North West      2
## 1711  2020-08-06               North West      2
## 1712  2020-08-07               North West      2
## 1713  2020-08-08               North West      2
## 1714  2020-08-09               North West      3
## 1715  2020-08-10               North West      2
## 1716  2020-08-11               North West      3
## 1717  2020-08-12               North West      0
## 1718  2020-08-13               North West      2
## 1719  2020-08-14               North West      2
## 1720  2020-08-15               North West      6
## 1721  2020-08-16               North West      2
## 1722  2020-08-17               North West      1
## 1723  2020-08-18               North West      2
## 1724  2020-08-19               North West      1
## 1725  2020-08-20               North West      1
## 1726  2020-08-21               North West      4
## 1727  2020-08-22               North West      3
## 1728  2020-08-23               North West      5
## 1729  2020-08-24               North West      4
## 1730  2020-08-25               North West      3
## 1731  2020-08-26               North West      4
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## 1734  2020-08-29               North West      0
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## 1738  2020-09-02               North West      2
## 1739  2020-09-03               North West      1
## 1740  2020-09-04               North West      3
## 1741  2020-09-05               North West      6
## 1742  2020-09-06               North West      1
## 1743  2020-09-07               North West      8
## 1744  2020-09-08               North West      6
## 1745  2020-09-09               North West      5
## 1746  2020-09-10               North West      5
## 1747  2020-09-11               North West      1
## 1748  2020-09-12               North West      4
## 1749  2020-09-13               North West      2
## 1750  2020-09-14               North West      4
## 1751  2020-09-15               North West      4
## 1752  2020-09-16               North West      6
## 1753  2020-09-17               North West      7
## 1754  2020-09-18               North West      6
## 1755  2020-09-19               North West      3
## 1756  2020-09-20               North West      2
## 1757  2020-09-21               North West      2
## 1758  2020-09-22               North West      9
## 1759  2020-09-23               North West     14
## 1760  2020-09-24               North West     10
## 1761  2020-09-25               North West      8
## 1762  2020-09-26               North West     14
## 1763  2020-09-27               North West     11
## 1764  2020-09-28               North West     15
## 1765  2020-09-29               North West     12
## 1766  2020-09-30               North West     17
## 1767  2020-10-01               North West     17
## 1768  2020-10-02               North West     20
## 1769  2020-10-03               North West     15
## 1770  2020-10-04               North West     15
## 1771  2020-10-05               North West     15
## 1772  2020-10-06               North West     20
## 1773  2020-10-07               North West     20
## 1774  2020-10-08               North West     22
## 1775  2020-10-09               North West     24
## 1776  2020-10-10               North West     31
## 1777  2020-10-11               North West     31
## 1778  2020-10-12               North West     35
## 1779  2020-10-13               North West     26
## 1780  2020-10-14               North West     35
## 1781  2020-10-15               North West     36
## 1782  2020-10-16               North West     34
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## 1786  2020-10-20               North West     48
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## 1788  2020-10-22               North West     49
## 1789  2020-10-23               North West     50
## 1790  2020-10-24               North West     51
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## 1792  2020-10-26               North West     53
## 1793  2020-10-27               North West     49
## 1794  2020-10-28               North West     57
## 1795  2020-10-29               North West     74
## 1796  2020-10-30               North West     73
## 1797  2020-10-31               North West     63
## 1798  2020-11-01               North West     76
## 1799  2020-11-02               North West     65
## 1800  2020-11-03               North West     77
## 1801  2020-11-04               North West     64
## 1802  2020-11-05               North West     67
## 1803  2020-11-06               North West     76
## 1804  2020-11-07               North West     79
## 1805  2020-11-08               North West     83
## 1806  2020-11-09               North West     82
## 1807  2020-11-10               North West     68
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## 1809  2020-11-12               North West     64
## 1810  2020-11-13               North West     81
## 1811  2020-11-14               North West     61
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## 1814  2020-11-17               North West     73
## 1815  2020-11-18               North West     71
## 1816  2020-11-19               North West     67
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## 1818  2020-11-21               North West     68
## 1819  2020-11-22               North West     52
## 1820  2020-11-23               North West     54
## 1821  2020-11-24               North West     64
## 1822  2020-11-25               North West     65
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## 1835  2020-12-08               North West     49
## 1836  2020-12-09               North West     48
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## 1841  2020-12-14               North West     51
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## 1852  2020-12-25               North West     52
## 1853  2020-12-26               North West     56
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## 1858  2020-12-31               North West     62
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## 1861  2021-01-03               North West     57
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## 1871  2021-01-13               North West     85
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## 1873  2021-01-15               North West     87
## 1874  2021-01-16               North West     83
## 1875  2021-01-17               North West     81
## 1876  2021-01-18               North West     92
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## 1878  2021-01-20               North West     89
## 1879  2021-01-21               North West     85
## 1880  2021-01-22               North West    110
## 1881  2021-01-23               North West    103
## 1882  2021-01-24               North West     95
## 1883  2021-01-25               North West     86
## 1884  2021-01-26               North West    102
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## 1888  2021-01-30               North West     77
## 1889  2021-01-31               North West     85
## 1890  2021-02-01               North West     96
## 1891  2021-02-02               North West     82
## 1892  2021-02-03               North West     71
## 1893  2021-02-04               North West     79
## 1894  2021-02-05               North West     67
## 1895  2021-02-06               North West     62
## 1896  2021-02-07               North West     53
## 1897  2021-02-08               North West     73
## 1898  2021-02-09               North West     69
## 1899  2021-02-10               North West     72
## 1900  2021-02-11               North West     67
## 1901  2021-02-12               North West     67
## 1902  2021-02-13               North West     62
## 1903  2021-02-14               North West     50
## 1904  2021-02-15               North West     56
## 1905  2021-02-16               North West     55
## 1906  2021-02-17               North West     55
## 1907  2021-02-18               North West     52
## 1908  2021-02-19               North West     40
## 1909  2021-02-20               North West     34
## 1910  2021-02-21               North West     36
## 1911  2021-02-22               North West     25
## 1912  2021-02-23               North West     35
## 1913  2021-02-24               North West     34
## 1914  2021-02-25               North West     22
## 1915  2021-02-26               North West     38
## 1916  2021-02-27               North West     26
## 1917  2021-02-28               North West     32
## 1918  2021-03-01               North West     31
## 1919  2021-03-02               North West     13
## 1920  2021-03-03               North West     22
## 1921  2021-03-04               North West     12
## 1922  2021-03-05               North West     25
## 1923  2021-03-06               North West     15
## 1924  2021-03-07               North West     23
## 1925  2021-03-08               North West     16
## 1926  2021-03-09               North West     14
## 1927  2021-03-10               North West     12
## 1928  2021-03-11               North West     17
## 1929  2021-03-12               North West     10
## 1930  2021-03-13               North West     11
## 1931  2021-03-14               North West     20
## 1932  2021-03-15               North West     16
## 1933  2021-03-16               North West     12
## 1934  2021-03-17               North West     11
## 1935  2021-03-18               North West      3
## 1936  2021-03-19               North West     12
## 1937  2021-03-20               North West     11
## 1938  2021-03-21               North West      7
## 1939  2021-03-22               North West      4
## 1940  2021-03-23               North West      2
## 1941  2020-03-01               South East      0
## 1942  2020-03-02               South East      0
## 1943  2020-03-03               South East      1
## 1944  2020-03-04               South East      0
## 1945  2020-03-05               South East      1
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## 2453  2020-07-03               South West      0
## 2454  2020-07-04               South West      0
## 2455  2020-07-05               South West      1
## 2456  2020-07-06               South West      0
## 2457  2020-07-07               South West      0
## 2458  2020-07-08               South West      2
## 2459  2020-07-09               South West      0
## 2460  2020-07-10               South West      1
## 2461  2020-07-11               South West      0
## 2462  2020-07-12               South West      0
## 2463  2020-07-13               South West      1
## 2464  2020-07-14               South West      0
## 2465  2020-07-15               South West      0
## 2466  2020-07-16               South West      0
## 2467  2020-07-17               South West      1
## 2468  2020-07-18               South West      0
## 2469  2020-07-19               South West      0
## 2470  2020-07-20               South West      0
## 2471  2020-07-21               South West      0
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## 2474  2020-07-24               South West      0
## 2475  2020-07-25               South West      0
## 2476  2020-07-26               South West      0
## 2477  2020-07-27               South West      0
## 2478  2020-07-28               South West      0
## 2479  2020-07-29               South West      0
## 2480  2020-07-30               South West      1
## 2481  2020-07-31               South West      0
## 2482  2020-08-01               South West      0
## 2483  2020-08-02               South West      0
## 2484  2020-08-03               South West      0
## 2485  2020-08-04               South West      0
## 2486  2020-08-05               South West      0
## 2487  2020-08-06               South West      0
## 2488  2020-08-07               South West      0
## 2489  2020-08-08               South West      0
## 2490  2020-08-09               South West      0
## 2491  2020-08-10               South West      0
## 2492  2020-08-11               South West      0
## 2493  2020-08-12               South West      0
## 2494  2020-08-13               South West      0
## 2495  2020-08-14               South West      1
## 2496  2020-08-15               South West      0
## 2497  2020-08-16               South West      0
## 2498  2020-08-17               South West      2
## 2499  2020-08-18               South West      0
## 2500  2020-08-19               South West      0
## 2501  2020-08-20               South West      0
## 2502  2020-08-21               South West      0
## 2503  2020-08-22               South West      0
## 2504  2020-08-23               South West      0
## 2505  2020-08-24               South West      0
## 2506  2020-08-25               South West      1
## 2507  2020-08-26               South West      0
## 2508  2020-08-27               South West      1
## 2509  2020-08-28               South West      0
## 2510  2020-08-29               South West      0
## 2511  2020-08-30               South West      0
## 2512  2020-08-31               South West      0
## 2513  2020-09-01               South West      0
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## 2515  2020-09-03               South West      0
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## 2517  2020-09-05               South West      0
## 2518  2020-09-06               South West      0
## 2519  2020-09-07               South West      0
## 2520  2020-09-08               South West      1
## 2521  2020-09-09               South West      0
## 2522  2020-09-10               South West      0
## 2523  2020-09-11               South West      0
## 2524  2020-09-12               South West      0
## 2525  2020-09-13               South West      1
## 2526  2020-09-14               South West      0
## 2527  2020-09-15               South West      0
## 2528  2020-09-16               South West      0
## 2529  2020-09-17               South West      1
## 2530  2020-09-18               South West      0
## 2531  2020-09-19               South West      0
## 2532  2020-09-20               South West      1
## 2533  2020-09-21               South West      0
## 2534  2020-09-22               South West      0
## 2535  2020-09-23               South West      0
## 2536  2020-09-24               South West      1
## 2537  2020-09-25               South West      0
## 2538  2020-09-26               South West      0
## 2539  2020-09-27               South West      0
## 2540  2020-09-28               South West      0
## 2541  2020-09-29               South West      0
## 2542  2020-09-30               South West      0
## 2543  2020-10-01               South West      0
## 2544  2020-10-02               South West      1
## 2545  2020-10-03               South West      0
## 2546  2020-10-04               South West      0
## 2547  2020-10-05               South West      0
## 2548  2020-10-06               South West      1
## 2549  2020-10-07               South West      0
## 2550  2020-10-08               South West      1
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## 2552  2020-10-10               South West      0
## 2553  2020-10-11               South West      4
## 2554  2020-10-12               South West      2
## 2555  2020-10-13               South West      0
## 2556  2020-10-14               South West      3
## 2557  2020-10-15               South West      1
## 2558  2020-10-16               South West      2
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## 2560  2020-10-18               South West      2
## 2561  2020-10-19               South West      2
## 2562  2020-10-20               South West      3
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## 2564  2020-10-22               South West      6
## 2565  2020-10-23               South West      5
## 2566  2020-10-24               South West      5
## 2567  2020-10-25               South West      5
## 2568  2020-10-26               South West      7
## 2569  2020-10-27               South West      6
## 2570  2020-10-28               South West      8
## 2571  2020-10-29               South West     11
## 2572  2020-10-30               South West      8
## 2573  2020-10-31               South West      5
## 2574  2020-11-01               South West      5
## 2575  2020-11-02               South West     11
## 2576  2020-11-03               South West      7
## 2577  2020-11-04               South West      8
## 2578  2020-11-05               South West      5
## 2579  2020-11-06               South West     11
## 2580  2020-11-07               South West     10
## 2581  2020-11-08               South West     10
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## 2583  2020-11-10               South West      6
## 2584  2020-11-11               South West     13
## 2585  2020-11-12               South West     17
## 2586  2020-11-13               South West      9
## 2587  2020-11-14               South West      8
## 2588  2020-11-15               South West     16
## 2589  2020-11-16               South West     18
## 2590  2020-11-17               South West     17
## 2591  2020-11-18               South West     26
## 2592  2020-11-19               South West     15
## 2593  2020-11-20               South West     25
## 2594  2020-11-21               South West     25
## 2595  2020-11-22               South West     24
## 2596  2020-11-23               South West     14
## 2597  2020-11-24               South West     20
## 2598  2020-11-25               South West     25
## 2599  2020-11-26               South West     16
## 2600  2020-11-27               South West     21
## 2601  2020-11-28               South West     35
## 2602  2020-11-29               South West     15
## 2603  2020-11-30               South West     22
## 2604  2020-12-01               South West     19
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## 2606  2020-12-03               South West     14
## 2607  2020-12-04               South West     20
## 2608  2020-12-05               South West     17
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## 2630  2020-12-27               South West     24
## 2631  2020-12-28               South West     21
## 2632  2020-12-29               South West     20
## 2633  2020-12-30               South West     17
## 2634  2020-12-31               South West     28
## 2635  2021-01-01               South West     29
## 2636  2021-01-02               South West     24
## 2637  2021-01-03               South West     28
## 2638  2021-01-04               South West     33
## 2639  2021-01-05               South West     31
## 2640  2021-01-06               South West     27
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## 2643  2021-01-09               South West     26
## 2644  2021-01-10               South West     34
## 2645  2021-01-11               South West     40
## 2646  2021-01-12               South West     53
## 2647  2021-01-13               South West     43
## 2648  2021-01-14               South West     39
## 2649  2021-01-15               South West     47
## 2650  2021-01-16               South West     57
## 2651  2021-01-17               South West     44
## 2652  2021-01-18               South West     47
## 2653  2021-01-19               South West     45
## 2654  2021-01-20               South West     65
## 2655  2021-01-21               South West     62
## 2656  2021-01-22               South West     61
## 2657  2021-01-23               South West     54
## 2658  2021-01-24               South West     59
## 2659  2021-01-25               South West     62
## 2660  2021-01-26               South West     47
## 2661  2021-01-27               South West     47
## 2662  2021-01-28               South West     52
## 2663  2021-01-29               South West     42
## 2664  2021-01-30               South West     39
## 2665  2021-01-31               South West     36
## 2666  2021-02-01               South West     29
## 2667  2021-02-02               South West     38
## 2668  2021-02-03               South West     32
## 2669  2021-02-04               South West     33
## 2670  2021-02-05               South West     25
## 2671  2021-02-06               South West     39
## 2672  2021-02-07               South West     36
## 2673  2021-02-08               South West     32
## 2674  2021-02-09               South West     31
## 2675  2021-02-10               South West     18
## 2676  2021-02-11               South West     20
## 2677  2021-02-12               South West     28
## 2678  2021-02-13               South West     29
## 2679  2021-02-14               South West     17
## 2680  2021-02-15               South West     22
## 2681  2021-02-16               South West     12
## 2682  2021-02-17               South West     20
## 2683  2021-02-18               South West     21
## 2684  2021-02-19               South West     19
## 2685  2021-02-20               South West     13
## 2686  2021-02-21               South West     16
## 2687  2021-02-22               South West     11
## 2688  2021-02-23               South West      6
## 2689  2021-02-24               South West     10
## 2690  2021-02-25               South West     12
## 2691  2021-02-26               South West      7
## 2692  2021-02-27               South West      6
## 2693  2021-02-28               South West     10
## 2694  2021-03-01               South West     15
## 2695  2021-03-02               South West      8
## 2696  2021-03-03               South West      3
## 2697  2021-03-04               South West      4
## 2698  2021-03-05               South West      4
## 2699  2021-03-06               South West      7
## 2700  2021-03-07               South West      1
## 2701  2021-03-08               South West      8
## 2702  2021-03-09               South West      4
## 2703  2021-03-10               South West      4
## 2704  2021-03-11               South West      2
## 2705  2021-03-12               South West      2
## 2706  2021-03-13               South West      5
## 2707  2021-03-14               South West      2
## 2708  2021-03-15               South West      3
## 2709  2021-03-16               South West      2
## 2710  2021-03-17               South West      4
## 2711  2021-03-18               South West      1
## 2712  2021-03-19               South West      1
## 2713  2021-03-20               South West      0
## 2714  2021-03-21               South West      4
## 2715  2021-03-22               South West      1
## 2716  2021-03-23               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2021-03-24"

The completion date of the NHS Pathways data is Wednesday 24 Mar 2021.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 15 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 15 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -19.203  -15.963   -4.630    6.325   32.741  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.230e+00  6.246e-02  83.742   <2e-16 ***
## note_lag    1.131e-05  1.210e-06   9.351   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 212.3538)
## 
##     Null deviance: 81952  on 334  degrees of freedom
## Residual deviance: 68267  on 333  degrees of freedom
##   (15 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  186.827697    1.000011
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 164.953324 210.728619
## note_lag      1.000009   1.000014

Rsq(lag_mod)
## [1] 0.1669873

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                             sysname 
##                                                                                            "Darwin" 
##                                                                                             release 
##                                                                                            "19.6.0" 
##                                                                                             version 
## "Darwin Kernel Version 19.6.0: Tue Jan 12 22:13:05 PST 2021; root:xnu-6153.141.16~1/RELEASE_X86_64" 
##                                                                                            nodename 
##                                                                           "Mac-1616665945887.local" 
##                                                                                             machine 
##                                                                                            "x86_64" 
##                                                                                               login 
##                                                                                              "root" 
##                                                                                                user 
##                                                                                            "runner" 
##                                                                                      effective_user 
##                                                                                            "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.4                         
## year           2021                        
## month          02                          
## day            15                          
## svn rev        80002                       
## language       R                           
## version.string R version 4.0.4 (2021-02-15)
## nickname       Lost Library Book

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.4 (2021-02-15)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.5     ggpubr_0.4.0         lubridate_1.7.10    
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.17             
##  [7] kableExtra_1.3.4     janitor_2.1.0        remotes_2.2.0       
## [10] projections_0.5.2    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.26          
## [16] reshape2_1.4.4       rvest_1.0.0          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.1        stringr_1.4.0       
## [22] dplyr_1.0.5          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.3          tibble_3.1.0         ggplot2_3.3.3       
## [28] tidyverse_1.3.0      here_1.0.1           reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.1   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.1.0      fansi_0.4.2       splines_4.0.4    
## [13] knitr_1.31        jsonlite_1.7.2    nloptr_1.2.2.2    broom_0.7.5      
## [17] dbplyr_2.1.0      compiler_4.0.4    httr_1.4.2        backports_1.2.1  
## [21] assertthat_0.2.1  Matrix_1.3-2      cli_2.3.1         htmltools_0.5.1.1
## [25] tools_4.0.4       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.6       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.6       svglite_2.0.0    
## [33] nlme_3.1-152      matchmaker_0.1.1  crosstalk_1.1.1   xfun_0.22        
## [37] ps_1.6.0          openxlsx_4.2.3    lme4_1.1-26       lifecycle_1.0.0  
## [41] statmod_1.4.35    rstatix_0.7.0     MASS_7.3-53       scales_1.1.1     
## [45] hms_1.0.0         parallel_4.0.4    sodium_1.1        yaml_2.2.1       
## [49] curl_4.3          gridExtra_2.3     stringi_1.5.3     highr_0.8        
## [53] kyotil_2020.10-12 boot_1.3-26       zip_2.1.1         rlang_0.4.10     
## [57] pkgconfig_2.0.3   systemfonts_1.0.1 evaluate_0.14     lattice_0.20-41  
## [61] labeling_0.4.2    htmlwidgets_1.5.3 cowplot_1.1.1     tidyselect_1.1.0 
## [65] plyr_1.8.6        magrittr_2.0.1    R6_2.5.0          generics_0.1.0   
## [69] DBI_1.1.1         mgcv_1.8-33       pillar_1.5.1      haven_2.3.1      
## [73] foreign_0.8-81    withr_2.4.1       survival_3.2-7    abind_1.4-5      
## [77] modelr_0.1.8      crayon_1.4.1      car_3.0-10        utf8_1.2.1       
## [81] rmarkdown_2.7     viridis_0.5.1     grid_4.0.4        readxl_1.3.1     
## [85] data.table_1.14.0 reprex_1.0.0      digest_0.6.27     webshot_0.5.2    
## [89] munsell_0.5.0     viridisLite_0.3.0